Shape measurement instrument and shape measurement method

ABSTRACT

A shape measurement instrument includes a plurality of transmitters  1  to  4  which radiate signals having different waveforms or phases, receivers  31  to  34  which receive signals reflected from an object O, correlation units  41  to  44  which obtain correlation waveforms between waveforms of the signals received by the receivers  31  to  34 , and the signal radiated by a transmitter radiating the received signal of the transmitters  1  to  4 , and a shape estimation unit  5  which extracts a quasi-wavefront based on the correlation waveforms obtained by the correlation units  41  to  44  and estimates a shape of the object O based on a relationship between the quasi-wavefront and the object O. As a result, a period of time required to measure an object shape can be significantly reduced.

RELATED APPLICATIONS

This application is the U.S. National Phase under 35 U.S.C. §371 ofInternational Application No. PCT/JP2008/001017, filed on Apr. 17, 2008,which in turn claims the benefit of Japanese Application Nos.2007-119101, filed on Apr. 27, 2007 and 2007-133957, filed on May 21,2007, the disclosures of which Applications are incorporated byreference herein.

TECHNICAL FIELD

The present invention relates to a shape measurement instrument formeasuring a shape of a target object by radiating a transmission signaland receiving a reflected wave of the transmission signal reflected fromthe object.

BACKGROUND ART

In order to find out an external environment of a mobile machine or thelike, such as a robot, an automobile, a ship, an aircraft or the like,from its inside or outside, it is important to recognize surroundingobjects and their shapes. In particular, when the mobile machine isallowed to automatically travel, shape recognition is more important interms of avoidance of danger or the like. Moreover, there is a largesocial demand for human shape estimation, which is applicable tosecurity services or care services. As means for estimating a shape ofan object, an imaging system employing radar has attracted attention.For example, a UWB radar, which utilizes an ultra-wide band (UWB)signal, can measure a shape of a near-field target at a high resolution,and therefore, has been used in many applications for ground probing andnondestructive testing. However, in conventional ground penetratingradar imaging, most estimation algorithms for estimating a shape from ameasurement result are based on iterative improvement, iterativecalculation or the like, and therefore, it takes a long time to completeshape estimation. Therefore, it is difficult to directly apply theconventional techniques to a real-time process required for theaforementioned robots and the like.

Therefore, the present inventors have developed and proposed ahigh-speed shape estimation algorithm which enables a real-time process,called SEABED (Shape Estimation Algorithm based on BST (BoundaryScattering Transform) and Extraction of Directly scattered waves). InSEABED, a shape of an object is estimated by utilizing a reversibleconversion relationship established between a relationship between atime delay of a scattered wave of a transmission signal which isobtained by changing a transmission/reception location, and thetransmission/reception location, and the shape of the object (e.g.,Patent Document 1 and Non-Patent Documents 1 to 5).

The principle of the SEABED method will be described below. FIG. 15 is adiagram for describing how antenna scanning is performed in the SEABEDmethod. In the SEABED method, it is assumed that an object to bemeasured (target object) is a physical object which has a clearboundary, and the boundary is measured to obtain a “quasi-wavefront.” Ashape of the target object is obtained by inverse-transforming thequasi-wavefront.

In the description of the principle, referring to FIG. 15, atwo-dimensional problem is dealt with, assuming that a target object Oand a transmission/receiving antenna A are provided in the same plane.It is also assumed that radio waves propagate as Transverse Electric(TE) waves. Space in which the target object O and thetransmission/receiving antenna A are located is referred to as “r-space(r-domain),” and if a set is expressed in r-domain, the set is referredto as an “expression in r-domain.” Also, a point in r-domain isexpressed as (x, y). Here, both x and y (y>0) are normalized using thecenter wavelength λ of a transmitted pulse in vacuum. Thetransmission/receiving antenna A is assumed to be omnidirectional, andrepeatedly transmit and receive monocycle pulses at measurementlocations x_(n) (n=1 to N (integers)) spaced at predetermined intervals(e.g., regular intervals) while scanning on the x-axis in r-domain. Inaddition, a reception electric field at a measurement location (x,y)=(X, 0) of the transmission/receiving antenna A is defined as s′(X,Y), and Y is defined as Y=(c×t)/(2×λ), where t is a period of time fromtransmission to reception, and c is the speed of light in vacuum. Notethat y>0 and therefore Y>0, and also, a time at which an instantaneousenvelope at a measurement location x_(n) of the transmission/receivingantenna A becomes maximum is assumed to be t=−0.

Moreover, for the purpose of removal of noise, a matched filter using atransmission waveform is applied to s′(X, Y) in the Y-direction, and areceived waveform obtained by the application of the matched filter isnewly set as s(X, Y). This s(X, Y) is used as data for obtaining a shapeof the target object O. Here, space expressed as (X, Y) is referred toas “d-space (d-domain),” and if a set is expressed in d-space, the setis referred to as an “expression in d-domain.” X and Y are normalizedusing the center wavelength and the center frequency of a transmittedpulse, respectively.

Changes in the complex permittivity ε(x, y) of the target object Ohaving a continuous boundary surface are assumed to be a set of aplurality of piecewise differentiable curves. Specifically, the complexpermittivity s(x, y) of the target object O is expressed as:

$\begin{matrix}{{{\nabla{ɛ( {x,y} )}}}^{2} = {\sum\limits_{q \in H}{a_{q}{\delta( {y - {g_{q}(x)}} )}}}} & ( {{Expression}\mspace{14mu} 1} )\end{matrix}$

Here, it is assumed that g_(q)(x) is a differentiable single-valuedfunction, and q={(x, y)|y=g_(q)(x), xεJq}εH, where Jq is the domain ofdefinition of the function g_(q)(x), a_(q) is a positive constantdepending on qεH, and H is the set of all q′s. Elements of H are “targetboundary surfaces.”

A subset P of d-space is defined as:P={(X,Y)|∂s(X,Y)/∂Y=0}  (Expression 2)

With respect to a connected closed set p⊂P, a domain I_(p) is definedas:I _(p)=[min_((X,Y)εp) X,max_((X,Y)εp) X]  (Expression 3)

A single-valued function f_(p)(X) is present which has the domain ofdefinition I_(p) with respect to p if there is only one Y satisfying (X,Y)εp with respect to an arbitrary XεI_(p), and satisfies Y=f_(p)(X). Aset of p′s for which the function f_(p)(X) is differentiable and|∂f_(p)(X)/∂X|≦1 is defined as G, and elements of G are referred to“quasi-wavefronts.”

When Expression (1) is satisfied, direct scattered waves from a boundaryhold information about a target boundary surface (expressing a surfaceand a shape of the target object O). This is similarly established in aknown medium having a constant propagation speed, although it ishereinafter assumed for the sake of simplicity that all propagationpaths of direct waves are in vacuum.

FIGS. 16( a) and 16(b) are diagrams for describing a boundary scatteringtransform. FIG. 16( a) shows an example of a change in complexpermittivity in r-domain, and FIG. 16( b) shows a quasi-wavefront ofd-domain corresponding to r-domain of FIG. 16( a).

If it is assumed that p corresponds to direct scattering from q, it canbe seen form FIG. 16( a) that a point (X, Y) on p is expressed asExpression (4) using a relationship between the length of a verticalline from the transmission/receiving antenna A to a curve Lq expressedby q, and a location of the transmission/receiving antenna A. Atransform expressed as Expression (4) is referred to as a boundaryscattering transform.

Only a time delay of a scattered wave, i.e., Y is observed at thelocation of the antenna A of FIG. 16( a), and a scattering point islocated somewhere on a circle whose center is A and whose radius is Y,however, an angle from which the scattered wave comes is unknown. Ycorresponds to a time delay of a scattered wave with respect to eachantenna location X. FIG. 16( b) shows a relationship between X and Y.

Note that a curve expressed by p may have a plurality of Y values withrespect to some X value. Symbols ◯ and Δ shown in FIG. 16( b) are anexample of such a case. These symbols ◯ and Δ correspond to symbols ◯and Δ shown in FIG. 16( a), respectively. The lengths of a solid lineand a dashed line of FIG. 16( a) are the same as those of FIG. 16( b),respectively. The solid line and the dashed line at an antenna locationP of FIG. 16( a) are both perpendicular to Lq. Points indicated bysymbols ◯ and Δ are scattering points of radio waves, which are receivedas scattered waves having different time delays in FIG. 16( b).

$\begin{matrix}\{ \begin{matrix}{X = {x + {y\frac{\mathbb{d}y}{\mathbb{d}x}}}} \\{Y = {y\sqrt{1 + ( \frac{\mathbb{d}y}{\mathbb{d}x} )^{2}}}}\end{matrix}  & ( {{Expression}\mspace{14mu} 4} )\end{matrix}$

Note that (x, y) is a point located on q.

By calculating an inverse transform of this boundary scatteringtransform, a shape of the target object O can be obtained from areceived waveform. This inverse transform is obtained as expressed asExpression (5). This inverse transform is referred to as an inverseboundary scattering transform.

$\begin{matrix}\{ \begin{matrix}{x = {X - {Y\frac{\mathbb{d}Y}{\mathbb{d}X}}}} \\{y = {Y\sqrt{1 - ( \frac{\mathbb{d}Y}{\mathbb{d}X} )^{2}}}}\end{matrix}  & ( {{Expression}\mspace{14mu} 5} )\end{matrix}$

Although two-dimensional measurement has been described above, theSEABED method can be easily extended to three-dimensional measurement.Also, although it has been assumed above that the transmission/receivingantenna A travels along a straight line, a transform expressioncorresponding to a case where the transmission/receiving antenna Atravels along any curves can be easily obtained.

For example, a boundary scattering transform for a three-dimensionalproblem is expressed as Expression (6), and its inverse transform isexpressed as Expression (7).

$\begin{matrix}\{ \begin{matrix}{X = {x + {z\frac{\partial z}{\partial x}}}} \\{Y = {y + {z\frac{\partial z}{\partial y}}}} \\{Z = {z\sqrt{1 + ( \frac{\partial z}{\partial x} )^{2} + ( \frac{\partial z}{\partial y} )^{2}}}}\end{matrix}  & ( {{Expression}\mspace{14mu} 6} ) \\\{ \begin{matrix}{x = {X - {Z\frac{\partial Z}{\partial X}}}} \\{y = {Y - {Z\frac{\partial Z}{\partial Y}}}} \\{z = {Z\sqrt{1 - ( \frac{\partial Z}{\partial X} )^{2} - ( \frac{\partial Z}{\partial Y} )^{2}}}}\end{matrix}  & ( {{Expression}\mspace{14mu} 7} )\end{matrix}$

In the SEABED method which estimates a shape of the target object O froma received waveform using Expression (5) (Expression (7) for athree-dimensional problem), the shape of the target object O isspecifically measured by executing the following process.

FIG. 17 is a flowchart showing a procedure when a shape of an object ismeasured by the SEABED method.

As shown in FIG. 17, in the conventional SEABED method, at eachmeasurement location x_(n) a shape measurement instrument (not shown)transmits a monocycle pulse (transmitted pulse), receives a reflectedwave of the transmitted pulse reflected from the target object O,performs analog-to-digital conversion (hereinafter abbreviated as “A/Dconversion”) with respect to the received wave, and stores the resultantwave, while scanning the omnidirectional transmission/receiving antennaA as shown in FIG. 15 (step S101).

Specifically, at a the measurement start location x₁, the shapemeasurement instrument initially transmits a monocycle pulse(transmitted pulse) from the omnidirectional transmission/receivingantenna A, receives a reflected wave of the transmitted pulse reflectedfrom the target object O, performs A/D conversion with respect to thereceived wave to generate a first received signal, and stores the firstreceived signal. After completing transmission and reception at themeasurement start location x₁, at a measurement location x₂ which is ata predetermined interval away from the measurement start location x₁ theshape measurement instrument transmits a monocycle pulse (transmittedpulse) from the transmission/receiving antenna A, receives a reflectedwave of the transmitted pulse reflected from the target object O,performs A/D conversion with respect to the received wave to generate asecond received signal, and stores the second received signal.Thereafter, similarly, at each measurement location x_(n) (from themeasurement start location x₁ to a measurement end location x_(N)), theshape measurement instrument transmits a monocycle pulse (transmittedpulse) from the transmission/receiving antenna A, receives a reflectedwave of the transmitted pulse reflected from the target object O,performs A/D conversion with respect to the received wave, and storesthe resultant received signal. Thus, the first received signal at themeasurement start location x₁ to an N-th received signal at themeasurement end location x_(N) are obtained.

Next, in step S102, the shape measurement instrument obtains across-correlation between a waveform of each of the first to N-threceived signals and a waveform of a reference signal, thereby obtainingfirst to N-th correlation waveforms corresponding to the first to N-threceived signals, respectively. A correlation function ρ(τ) is expressedas:ρ(τ)=∫s(t)·r(t+τ)dt  (Expression 8)where τ is the time delay, r(t) is the reference signal, and s(t) is thereceived signal. Note that the integration range is a range within whichthe received signal s(t) exists.

Here, the waveform of the reference signal is the waveform of thetransmitted pulse, which is based on the assumption that the waveform ofthe received signal has the same shape as that of the transmitted pulse.A process in this step corresponds to application of a matched filter tothe received signal.

Next, in step S103, the shape measurement instrument obtains extremums(relative maximums and relative minimums) in the first to N-thcorrelation waveforms.

Next, in step S104, the shape measurement instrument connects adjacentextremums. More specifically, the shape measurement instrument connectsextremums in a manner which satisfies Expression (9):−1≦(location of extremum M _(n)−location of extremum M_(n-1))/(measurement location X _(n)−measurement location X_(n-1))≦1  (Expression 9)

Here, the location of extremum M_(n) is a location in an XY plane of anextremum obtained from an n-th correlation waveform obtained at themeasurement location x_(n). A curve obtained by connecting the extremumsin this manner is a quasi-wavefront.

Next, in step S105, the shape measurement instrument extracts a truequasi-wavefront. The quasi-wavefront obtained by the process of stepS104 includes undesired quasi-wavefronts, such as one which is generateddue to noise, one which is generating by extracting a vibrationcomponent, one which is generated due to multiple scattering, and thelike. Therefore, it is necessary to remove these undesiredquasi-wavefronts so as to extract a true quasi-wavefront which trulyindicates a boundary surface of the object O. In this process ofextracting a true quasi-wavefront, an evaluation value w_(p) which isdefined as Expression (10) is firstly used to select and extract aquasi-wavefront having an evaluation value w_(p) which is larger than apredetermined threshold α. If the threshold α is excessively small, alarge number of undesired quasi-wavefronts are included. If thethreshold a is excessively large, true quasi-wavefronts are alsoremoved. Therefore, the threshold α is experimentally or empirically setin view of the maximum value of the evaluation value w_(p).w _(p)=|∫_(xεI) _(p) s(X,f _(p)(X))dX| ²  (Expression 10)

The evaluation value w_(p) takes a large value when a received signal ona quasi-wavefront has a large amplitude, and the domain of definition off_(p)(X) is wide.

Here, if only Expression (10) is used to extract true quasi-wavefronts,then when a quasi-wavefront caused by, for example, noise is locatedclose to a true quasi-wavefront, the evaluation value w_(p) may be largeand therefore the quasi-wavefront may not be removed. Therefore, when(x, y)εp₁ and (x, y)εp₂ are established where p₁, p₂εG, p₁≠p₂ andw_(p1)≦w_(p2), quasi-wavefronts are divided, i.e., p₁→p_(1′), p_(1″)(note that p_(1′)∪p_(1″)=p₁ and p_(1′)∩p_(1″)=p₁∩p₂) to obtain theevaluation value w_(p), thereby removing undesired quasi-wavefronts.

Thereafter, in the true quasi-wavefront extraction process, F_(p) (knownas a first Fresnel zone) expressed as Expression (11) and a newevaluation value W_(p) defined as Expression (12) are secondly used toselect and extract a quasi-wavefront having an evaluation value W_(p)larger than a predetermined threshold β. If the threshold β isexcessively small, a large number of undesired quasi-wavefronts areincluded. If the threshold β is excessively large, true quasi-wavefrontsare also removed. Therefore, the threshold β is experimentally orempirically set in view of the maximum value of the evaluation valueW_(p).

$\begin{matrix}{F_{p} = \begin{Bmatrix} ( {x_{0},y_{0}} ) \middle| {\sqrt{( {x - x_{0}} )^{2} + ( {y - y_{0}} )^{2}} +}  \\{\sqrt{( {x - X} )^{2} + y^{2}} < {1/2}}\end{Bmatrix}} & ( {{Expression}\mspace{14mu} 11} ) \\{W_{p} = {w_{p} - {\sum\limits_{{q \neq p} \in G}{w_{q}\frac{{\int_{({x,y})}^{\;}{\in {\mathcal{B}\lbrack q\rbrack}}},{F_{p}\ {\xi(x)}{\mathbb{d}x}}}{\int_{x \in I_{q}}^{\;}{{\xi(x)}\ {\mathbb{d}x}}}}}}} & ( {{Expression}\mspace{14mu} 12} )\end{matrix}$

The evaluation value W_(p) takes a smaller value when another boundarysurface having a large value is located in the Fresnel zone of somequasi-wavefront. ξ(x) is a weight function. For example, for the sake ofsimplicity, ξ(x) is set to ξ(x)=1.

A true quasi-wavefront thus extracted is a set of time periods fromtransmission of transmitted pulses at respective measurement locationsuntil reflected waves of the transmitted pulses which impinge on and arereflected from tangent planes of a surface of the target object O aredirectly received.

Next, in step S106, the shape measurement instrument obtains the shapeof the object O from the true quasi-wavefronts extracted in step S105using Expression (5).

Thus, in the SEABED method, the shape of the target object O can bedirectly estimated by the inverse transform expressed as Expression (5).Therefore, the shape of the object O can be considerably quicklymeasured.

In the SEABED method described above, a shape can be estimated by theinverse boundary scattering transform expressed as Expression (5) or(7). An image obtained by the inverse boundary scattering transform isnot an approximate solution and is a mathematically exact solution, andcan be directly obtained rather than based on iterative calculation.These advantages enable the SEABED method to be an imaging algorithmcapable of calculation at higher resolution than those of conventionalmethods and at considerably high speed.

Patent Document 1: Japanese Laid-Open Patent Publication No. 2006-343205

Non-Patent Document 1: Takuya SAKAMOTO and Tom SATO, “A NonparametricTarget Shape Estimation Algorithm for UWB Pulse Radar Systems,”TECHNICAL REPORT OF IEICE, A•P2003-36, vol. 103, no. 120, pp. 1-6, Jun.19, 2003

Non-Patent Document 2: Takuya SAKAMOTO and Tom SATO, “A PhaseCompensation Algorithm for High-Resolution Shape Estimation Algorithmswith Pulse Radars,” TECHNICAL REPORT OF IEICE, A•2004-72, vol. 104, no.202, pp. 37-42, Jul. 22, 2004

Non-Patent Document 3: Takuya SAKAMOTO and Tom SATO, “A Target ShapeEstimation Algorithm for Pulse Radar Systems based on BoundaryScattering Transform,” IEICE TRANSACTIONS on Communications, Vol. E87-B,No. 5, May 2004, pp. 1357-1365

Non-Patent Document 4: Shouhei KIDERA, Takuya SAKAMOTO and Toru SATO, “AFast Imaging Algorithm with Bi-static Antenna for UWB Pulse RadarSystems,” 34-th Electromagnetic Theory Symposium of IEICE, EMT-05-58,November 2005

Non-Patent Document 5: Shouhei Kidera, Takuya Sakamoto and Toru Sato, “AHigh-resolution 3-D Imaging Algorithm with Linear Array Antennas for UWBPulse Radar Systems,” IEEE AP-S International Symposium, USNC/URSINational Radio Science Meeting, AMEREM Meeting, pp. 1057-1060, July,2006

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention

However, in the SEABED method, it is necessary to move atransmission/receiving antenna when a signal is transmitted andreceived. In addition, it is necessary to move thetransmission/receiving antenna at low speed so as to obtain asufficiently high signal-to-noise power ratio for analysis. Therefore,the measurement requires a long time, and therefore, the advantage ofhigh-speed processing of the SEABED method is not exhibited, resultingin a disadvantage that it takes a long time to perform the overallprocess from the measurement to the shape estimation.

An object of the present invention is to provide a shape measurementsystem capable of measuring a target object quickly.

Solution to the Problems

A shape measurement instrument of the present invention includes aplurality of transmitters configured to generate signals expressed as afunction system having a low cross-correlation value which is similar toan orthogonal function system or a quasi-orthogonal function system, andradiate the signals having different waveforms or phases, a receiverconfigured to receive the signal reflected from a target object, acorrelation unit configured to obtain a correlation waveform of awaveform of the signal received by the receiver and the signal radiatedby the transmitter radiating the received signal of the plurality oftransmitters, and a shape estimation unit configured to extract aquasi-wavefront based on a plurality of the correlation waveformsobtained by the correlation unit, and estimate a shape of the targetobject based on a relationship between the quasi-wavefront and the shapeof the target object.

With this configuration, the transmitters can simultaneously radiatesignals, and the receiver can demodulate the signals. Therefore, thetransmitters do not need to be scanned and a shape of a target objectcan be estimated by performing measurement once. Therefore, a period oftime required for measurement can be significantly reduced.

In particular, the transmitters and the receiver may be provided atsubstantially the same location. In this case, a so-called SEABED methodcan be used to increase the speed of an estimation algorithm andtherefore increase the overall speed of measurement and calculation(real-time imaging).

Moreover, a signal having a fractional bandwidth (a ratio of an occupiedbandwidth to a center frequency) of 20% or more or a UWB signal may beused as the transmission signal. In this case, a shape of an object canbe measured with higher accuracy. Also, a carrier wave (sine wave)modulated using a digital signal having a binary value including apositive value and a negative value may be used instead of a basebandsignal.

Moreover, a pseudonoise sequence code (PN code) may be used as thetransmission signal. In this case, a broad-band and high-resolutionsignal can be obtained. For example, if an M-sequence having a highautocorrelation is used as the pseudonoise sequence, a shape measurementinstrument having a broad dynamic range can be achieved.

Also, an M-sequence may be used as the pseudonoise sequence andM-sequence codes having different phases may be assigned as signals ofthe transmitters. In this case, a large number of transmitters can besimultaneously used.

Also, a Gold sequence may be used as the pseudonoise sequence. In thiscase, a large number of transmitters can be simultaneously used withoutsynchronization. Also, the degreed of freedom of selection of acombination of optimum codes for an imaging system is increased.

Also, a Kasami sequence may be used as the pseudonoise sequence. In thiscase, a larger number of transmitters can be simultaneously used thanwhen a Gold sequence is used. The resolution of an obtained image can beincreased by increasing the number of transmitters.

Also, when the transmitters and the receiver are provided at differentlocations, a revised SEABED method which is obtained by revising theSEABED method may be used. In this case, the speed of the estimationalgorithm can be increased, and the overall speed of measurement andcalculation can be increased (real-time imaging).

As a result, when an expensive receiver, such as a weather radar, aradar for astronomical observatory or the like, is used, the number ofreceivers can be reduced, resulting in lower cost.

Alternatively, signals of a plurality of transmitters may be received bya plurality of receivers. In this case, the amount of information can beincreased while the system includes a smaller number of transmitters andreceivers, whereby high-accuracy measurement can be performed withrelatively low cost.

A shape measurement method of the present invention employs a shapemeasurement instrument including a plurality of transmitters, a receiverconfigured to receive a signal reflected from a target object, acorrelation unit, and a shape estimation unit. The method includes thesteps of (a) radiating signals having different waveforms or phasesexpressed as an orthogonal function system or a quasi-orthogonalfunction system by the plurality of transmitters, (b) receiving thesignals reflected from the target object by the receiver, (c) obtaininga correlation waveform of a waveform of the signal received by thereceiver and the signal radiated by the transmitter radiating thereceived signal of the plurality of transmitters, by the correlationunit, (d) obtaining the time delays which give an extremum of thecorrelation waveform by the shape estimation unit, (e) connectingadjacent ones of the delays which give an extremum to generate aquasi-wavefront by the shape estimation unit, (f) extracting a truequasi-wavefront from the quasi-wavefront by the shape estimation unit,and (g) estimating a shape of the target object from the truequasi-wavefront by the shape estimation unit.

According to this method, the transmitters output signals havingdifferent phases or waveforms, whereby the transmitters cansimultaneously output the signals. Therefore, a shape of an object canbe estimated by performing measurement once, resulting in a reduction ina period of time required for measurement.

Shape estimation may be performed using the SEABED method or the revisedSEABED method, depending on the locations of a receiver and atransmitter. In this case, a calculation time required for shapeestimation can be significantly reduced.

Effect of the Invention

Thus, the shape measurement instrument of the present invention canacquire data by performing measurement once, whereby real-time imagingcan be achieved.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing an example circuit configuration in a shapemeasurement instrument using electromagnetic waves according to a firstembodiment of the present invention.

FIG. 2 is a diagram showing a circuit configuration in a shapemeasurement instrument according to a second embodiment of the presentinvention.

FIGS. 3( a) and 3(b) are diagrams for describing a difference inarrangement of receiving and transmitting antennas between aconventional SEABED method and a revised SEABED method used in thisembodiment.

FIG. 4 is a diagram showing a model of a part of a shape measurementinstrument according to a third embodiment of the present invention.

FIG. 5 is a diagram showing a k-stage linear feedback shift registerwhich generates PN codes.

FIG. 6 is a diagram showing an output signal when a correlation processof a received signal and each Gold sequence code in the shapemeasurement instrument of the third embodiment.

FIG. 7 is a diagram showing an estimated shape of a target object and areal shape of the target object when an influence of direct waves is notremoved.

FIG. 8 is a diagram showing a received signal obtained by despreadingdirect waves.

FIG. 9 is a diagram showing a received signal, where direct waves have apower which is larger than scattered waves by about 10 dB.

FIG. 10 is a diagram showing a shape of a target object which isestimated using the received signal of FIG. 9.

FIG. 11 shows a relationship between the number of times of call of anevaluation function and an evaluation value.

FIG. 12 is a diagram showing a signal obtained by despreading directwaves using codes used in a measurement method according to a fourthembodiment.

FIG. 13 is a diagram showing a received signal including scattered wavesin the measurement method of the fourth embodiment.

FIG. 14 is a diagram showing an estimated shape obtained by the revisedSEABED method using the received signal of FIG. 13.

FIG. 15 is a diagram for describing how antenna scanning is performed inthe SEABED method.

FIGS. 16( a) and 16(b) are diagrams for describing a boundary scatteringtransform.

FIG. 17 is a flowchart showing a procedure when a shape of an object ismeasured by the SEABED method.

DESCRIPTION OF THE REFERENCE CHARACTERS

O, 20 object

2, 4, 6 transmitting antenna

5 shape estimation circuit

7, 12, 14, 16, 18, 19 receiving antenna

8 receiving circuit

9 shape estimation circuit

11, 13, 15, 17 transmitting antenna

21, 22, 23, 24 signal generator

31, 32, 33, 34 receiver

41, 42, 43, 44 correlating circuit

51, 52, 53, 54 radar

BEST MODE FOR CARRYING OUT THE INVENTION

(First Embodiment)

Hereinafter, a first embodiment of the present invention will bedescribed with reference to the accompanying drawings.

FIG. 1 is a diagram showing an example circuit configuration in a shapemeasurement instrument using electromagnetic waves according to thefirst embodiment of the present invention.

The shape measurement instrument of this embodiment includes a pluralityof radars and a shape estimation circuit as shown in FIG. 1.Specifically, the shape measurement instrument of this embodimentincludes radars 51, 52, 53 and 54 provided at different locations and ashape estimation circuit 5 which receives signals output from the radars51 to 54. Each of the radars 51 to 54 has a signal generator whichgenerates an electrical signal, a transmitting antenna which radiatesthe electrical signal generated by the signal generator as a transmittedradio wave into space, a receiving antenna which receives a reflectedwave of the transmitted radio wave reflected from a target object O, areceiver which receives a received wave, and a correlating circuit whichreceives an output of the receiver. Specifically, the radar 51 has asignal generator 21, a transmitting antenna 11, a receiving antenna 12,a receiver 31, and a correlating circuit 41. The radar 52 has a signalgenerator 22, a transmitting antenna 13, a receiving antenna 14, areceiver 32, and a correlating circuit 42. The radar 53 has a signalgenerator 23, a transmitting antenna 15, a receiving antenna 16, areceiver 33, and a correlating circuit 43. The radar 54 has a signalgenerator 24, a transmitting antenna 17, a receiving antenna 18, areceiver 34, and a correlating circuit 44. Note that the number ofradars is not limited to four and may be more than four. Although anexample in which the radars 51 to 54 are arranged on a line in a planeas shown in FIG. 1 for the sake of simplicity will be described, radarsmay be arranged in a two-dimensional array so as to two-dimensionallymeasure a shape of the object O. Although the transmitting antenna andthe receiving antenna are preferably separately provided when a code isused, a single antenna may be used for both transmission and reception.Note that the transmitted radio wave preferably has a fractionalbandwidth (a ratio of an occupied bandwidth to a center frequency) of20% or more.

Next, measurement operation of, for example, the radar 51 will bedescribed. Initially, the signal generator 21 generates, for example, a26 GHz-band sine wave (carrier wave), and modulates the carrier waveusing a pseudonoise (PN) code (spread spectrum). As a modulation method,phase modulation is performed, for example. For example, the carrierwave and the pseudonoise code are input and multiplied in a doublebalanced mixer circuit including Gilbert cells, whereby aphase-modulated transmission signal can be easily generated. A signalwhich is radiated as a transmitted wave from the transmitting antenna 11is reflected on the object O, and a part of the signal is received bythe receiving antenna 12. Thereafter, a received wave output from thereceiving antenna 12 may be subjected to amplification, shaping(filtering) or the like in the receiver 31 before being transferred as areceived signal to the correlating circuit 41. The correlating circuit41 obtains a correlation between the received signal and the referencesignal to obtain a correlation waveform. Specifically, the receivedsignal is demodulated using the same PN code as that for thetransmission signal (so-called despreading), and is down-converted usingthe carrier wave, thereby obtaining the correlation waveform.

The radars 52 to 54 also simultaneously perform operation similar tothat of the radar 51, and transfer respective correlation waveforms tothe shape estimation circuit 5. Places where the radars 51 to 54 areplaced are directly used as measurement locations, whereby correlationwaveforms at the first to fourth measurement locations are obtained.Next, as in the aforementioned SEABED method, the shape estimationcircuit 5 obtains a location where a relative maximum of the absolutevalues of the correlation waveforms is obtained, extracts aquasi-wavefront, and outputs a shape of the object using the inverseboundary scattering transform.

Specifically, extremums in the correlation waveforms output from theradars 51 to 54 are obtained, and thereafter, adjacent extremums areconnected in a manner which satisfies Expression (9). Next, theevaluation value w_(p) defined as Expression (10) is used to select andextract a quasi-wavefront having an evaluation value larger than apredetermined threshold α. Here, when (x, y)εp₁ and (x, y)εp₂ areestablished where p₁, p₂εG, p₁≠p₂ and w_(p1)≦w_(p2), quasi-wavefrontsare divided, i.e., p₁→p_(1′), p_(1″) (note that p_(1′)∪p_(1″)=p₁ andp_(1′)∩p_(1″)=p₁∩p₂) to obtain the evaluation value w_(p), therebyremoving undesired quasi-wavefronts. Moreover, F_(p) expressed asExpression (11) and the new evaluation value W_(p) defined as Expression(12) are used to select and extract a quasi-wavefront having anevaluation value W_(p) larger than a predetermined threshold β. As aresult, a true quasi-wavefront is obtained. Next, the shape estimationcircuit 5 obtains a shape of the object O from the true quasi-wavefrontusing Expression (5).

Note that, in the shape measurement instrument of this embodiment, ifthe transmitting antennas are assigned different PN codes, then evenwhen a plurality of radars (transmitters) simultaneously transmitelectrical signals, and a receiving antenna simultaneously receives anelectrical signal transmitted from its own radar and an electricalsignal transmitted from a different radar, the radar can extract its ownsignal by performing despreading using its own transmission code. Inother words, according to the shape measurement instrument of thisembodiment and its measurement method, data of all the measurementlocations can be simultaneously obtained without changing the operationsof the radars, whereby a measuring time period for imaging can bereduced to about ¼ of that which is required when the radars arechanged. Although four radars are used in this embodiment,higher-accuracy imaging can be achieved by increasing the number ofradars. Also in this case, the radars can simultaneously performmeasurement, and therefore, the increase in measuring time period can besuppressed irrespective of the increase in accuracy.

For example, if M-sequence codes, which have excellent autocorrelation,are used as the PN codes, the measurement dynamic range of each radarcan be broadened, resulting in higher-accuracy imaging. Also, the numberof M-sequence codes having a low cross-correlation value is limited, andtherefore, when the number of radars is large, the outputs of the radarsmay be synchronized and the same M-sequence codes having differentphases may be assigned to the radars. As a result, even when a largernumber of radars are used, simultaneous measurement can be achieved. Inaddition, as the same M-sequence is used, suppression ofcross-correlation between different radars can be achieved in additionto the excellent autocorrelation characteristic of the M-sequence.

Moreover, when Gold codes, each of which is a combination of M-sequencecodes, are used as the PN codes, the number of codes can be dramaticallyincreased without establishing the aforementioned synchronization. As aresult, codes can be selected with a high degree of freedom, dependingon the purpose of the system, as described below. Alternatively, byusing Kasami sequences as the PN codes, a larger number of transmitters(transmitting antennas) can be simultaneously used than that when Goldsequences are used. The increase in the number of transmitters canincrease the resolution of an obtained image.

Although a case where radars output PN codes has been described above,the radars may output a quasi-orthogonal function system which issimilar to an orthogonal function system and in which the minimum anglebetween functions is, for example, 80, 70, 60, 50 degrees or the like,in addition to the orthogonal function system in which the angle betweenany two of all functions is 90 degrees. Here, the quasi-orthogonalfunction system refers to a function system in which the minimum anglebetween functions is 50 degrees or more (i.e., a low cross-correlationvalue), or a function system in which functions have a cross-correlationvalue which is low but does not cause the functions to hinder operationof each other. Signals expressed by the quasi-orthogonal function systeminclude those which are modulated using an M-sequence code, a Goldsequence code or the like. By using these signals in the shapemeasurement instrument, the effect of reducing the measuring time periodcan be obtained.

Note that the shape measurement instrument of this embodiment can beemployed in automobiles, robots, and other various machines. Whentwo-dimensionally arranged radars are used in an automobile, thelocations of the radars are changed with time due to movement of theautomobile, whereby a three-dimensional shape of the object O can bemeasured. Therefore, a target object can be determined to some extent,which can contribute to an improvement in safety during driving theautomobile.

(Second Embodiment)

FIG. 2 is a diagram showing a circuit configuration in a shapemeasurement instrument according to a second embodiment of the presentinvention. As shown in FIG. 2, the shape measurement instrument of thisembodiment includes a plurality of transmitting circuits each having atransmitting antenna, a single receiving circuit and correlatingcircuit, and an object shape estimation circuit. The transmittingcircuits have respective transmitting antennas 2, 4 and 6, and each havea signal generation circuit. Also, the functions and operation of thereceiving antenna 7 and the receiving circuit 8 are similar to those ofthe receiving antenna and the receiver of the first embodiment of FIG.1, and the function and operation of the correlating circuit are alsosimilar to those of the correlating circuit of the first embodiment.

The shape estimation circuit 9 has a function and operation basicallysimilar to those of the shape estimation circuit 5 of FIG. 1. Thereceiving circuit 8 and the correlating circuit demodulate reflectedwaves of transmitted waves which have been modulated using differentcodes, using codes which are assigned to the respective transmittingcircuits, to obtain correlations with the respective transmitted waves.The selection of codes and the method for modulation are similar tothose of the shape measurement instrument of the first embodiment.

In the second embodiment, a single receiving antenna, receiving circuitand correlating circuit are provided for a plurality of transmittingantennas and transmitting circuits, whereby the entire system can besimplified and its cost can be reduced. In particular, when radars areused to measure an object which is located at a great distance, areceiving circuit is more expensive than a transmitting circuit, andtherefore, the configuration of this embodiment allows a significantreduction in cost.

Note that the inverse transform expression (Expression (5)) in theSEABED method described in the BACKGROUND ART section is establishedunder the assumption of a monostatic radar in which the receivingantenna and the transmitting antenna are provided at the same location,and therefore, cannot be directly used when the transmitting antenna andthe receiving antenna are provided at different locations as in thisembodiment. However, by extending the SEABED method to a bi-static modelas described below, a solution can be directly obtained using an inversetransform expression as in the first embodiment or the like.Hereinafter, the SEABED method thus revised (hereinafter referred to asa “revised SEABED method”) will be described.

FIGS. 3( a) and 3(b) are diagrams for describing a difference inarrangement of receiving and transmitting antennas between aconventional SEABED method and a revised SEABED method used in thisembodiment. In the antenna arrangement of the conventional SEABED methodof FIG. 3( a), a transmitting antenna which transmits a signal and areceiving antenna which receives the signal are provided atsubstantially the same locations no matter whether an antenna is scannedor antennas are provided in an array. However, in the revised SEABEDmethod, a receiving antenna is fixed to a single location even if thelocation of a transmitting antenna is changed. In such a case, a revisedboundary scattering transform is provided which is expressed as:

$\begin{matrix}{{X = \frac{{( {x^{2} - y^{2}} )\overset{.}{y}} - {{xy}( {1 - {\overset{.}{y}}^{2}} )}}{{2x\overset{.}{y}} - {y( {1 - {\overset{.}{y}}^{2}} )}}}{Y = {\frac{1}{2}\{ {\sqrt{x^{2} + y^{2}} + \sqrt{y^{2} + \frac{( {x^{2} + y^{2}} )^{2}{\overset{.}{y}}^{2}}{( {y - {2x\overset{.}{y}} - {y{\overset{.}{y}}^{2}}} )^{2}}}} \}}}} & ( {{Expression}\mspace{14mu} 13} )\end{matrix}$where 2Y is a distance corresponding to a time delay with respect to atransmitting antenna location (2X, 0) and a receiving antenna location(0, 0).

Here, a character y with a dot thereon is a derivative dy/dx. In thisspecification, the character y with a dot thereon is also denoted as y′.

An ellipse whose major axis has a length of 2Y (2Y is the time delaymultiplied by the speed of light) and whose focuses are a receivingantenna location (0, 0) and a transmitting antenna location (2X, 0) isexpressed as F(x, y, X)=0. Note that F(x, y, X) is expressed as:

$\begin{matrix}{{F( {x,y,X} )} = {\frac{( {x - X} )^{2}}{Y^{2}} + \frac{y^{2}}{Y^{2} - X^{2}} - 1}} & ( {{Expression}\mspace{14mu} 14} )\end{matrix}$

Here, Y is a function of X and therefore is not explicitly indicated asan independent variable of F. An envelope which is drawn by the ellipsewhen the parameter X corresponding to the location of a middle pointbetween the transmitting and receiving antennas is changed, satisfiesthe following two expressions (Expression (15)).F(x,y,X)=0∂F(x,y,X)/∂X=0  (Expression 15)

Note that the partial derivative by X in Expression (15) means that itis independent of x and y, not of Y. By solving the simultaneousequations for x and y, an inverse revised boundary scattering transformis expressed as:

$\begin{matrix}{{x = \frac{{( {X^{2} + Y^{2}} )\overset{.}{Y}} - {2{XY}}}{{X\overset{.}{Y}} - Y}}{y = {{\frac{Y^{2} - X^{2}}{Y - {X\overset{.}{Y}}}}\sqrt{1 - \overset{.}{Y^{2}}}}}} & ( {{Expression}\mspace{14mu} 16} )\end{matrix}$

Here, a character Y with a dot thereon is a derivative dY/dX. In thisspecification, the character Y with a dot thereon is also denoted as Y′.

The use of Expression (16) allows high-speed estimation of a shape of atarget object in the shape measurement instrument of this embodiment aswell, which makes it possible to perform real-time imaging.

In the description above, expressions for transform are shown for theSEABED method in which transmission and reception are performed in thesame location and transmission/reception locations are changed, and inthe revised SEABED method in which only transmission locations arechanged while a reception location is fixed or in which only receptionlocations are changed while a transmission location is fixed. Incontrast to this, when transmission and reception locations are scannedwhile these locations are spaced apart at a predetermined distance, atwo-dimensional transform expression for imaging derived in Non-PatentDocument 4 can be applied to the shape measurement instrument of thepresent invention. Specifically, the conventional SEABED method isapplied to a case where the transmitting antenna 11 and the receivingantenna 12 of FIG. 1 are sufficiently close to each other so that adistance between the antennas can be neglected. When the distancebetween the antennas needs to be taken into consideration, it isnecessary to use an expression in which the predetermined distancebetween transmission and reception locations is taken intoconsideration. Moreover, in the case of a three-dimensional arrangement,a transform expression described in Non-Patent Document 5 can be used.

Moreover, also when transmission locations and reception locations arescanned along respective separate curves, an envelope of ellipsescorresponding to a plurality of transmission and reception locations canbe derived under a condition that a partial derivative by a variablewhich varies during scanning is zero, where the focuses of each ellipseare a transmission point and a reception point. An expression expressingthis envelope is a transform expression for generalized imagingcorresponding to each case, and therefore, a generalized SEABED methodwhich supports scanning of transmission and reception locations along anarbitrary curve is contemplated. Also for the generalized SEABED method,the present invention capable of significantly reducing a period of timerequired for scanning by assigning a plurality of codes to a pluralityof transmission locations is effective. The effectiveness of the presentinvention is not limited to the techniques in which the specifictransform expressions described herein are used.

(Third Embodiment)

A more specific example of the present invention including a code willbe described using a model shown in FIG. 3.

FIG. 4 is a diagram showing a model of a part of a shape measurementinstrument according to a third embodiment of the present invention. Theshape measurement instrument of this embodiment has a configurationincluding a plurality of transmitting circuits and a single fixedreceiving circuit as in the shape measurement instrument of the secondembodiment. In FIG. 4, for the sake of simplicity, the transmittingcircuits and the receiving circuit are each represented only by anantenna. FIG. 4 shows an example in which first to eighteenthtransmitting antennas and a single receiving antenna 19 for measuring anobject 20 are provided. The shape measurement instrument of thisembodiment has basically the same configuration as that of the objectestimation apparatus of the second embodiment. The shape measurementinstrument also includes an A/D converter and a memory.

In this system, the single receiving antenna receives signals from theeighteen transmitting antennas. Also, the transmitting antennas and thereceiving antenna are assumed to be omnidirectional antennas. Also, thetransmitting antennas transmit UWB signals which are spread usingpseudonoise sequences, in a baseband without using a carrier wave.Signals obtained by the receiving antenna are subjected to A/Dconversion before being stored into the memory.

In the description which follows, for the sake of simplicity, atwo-dimensional problem is dealt with and the mode of electromagneticwaves is assumed to be the TE mode. It is assumed that a target (objectto be measured) and the antennas are located in a plane, and the targethas a clear boundary. Space in which the target and the antennas arelocated is referred to as real space. A point in the real space isexpressed as (x, y). Here, both x (>0) and y (>0) are normalized by acenter wavelength λ, of a transmitted pulse in vacuum. A location of thereceiving antenna is assumed to be an origin (x, y)=(0, 0), and thetransmitting antennas are assumed to be located on an x-axis in the realspace. An output of a matched filter applied to a received signal at alocation (x, y)(2X, 0) of a transmitting antenna is defined as s(X, Y).Note that Y is defined as Y=ct/(2λ) where t is a period of time whichhas elapsed since transmission and c is the speed of light in vacuum.Since y>0, Y>0 is established. Space expressed as (X, Y) is referred toas data space, and an equiphase curve in the data space is referred toas a quasi-wavefront. Here, X and Y are normalized by a centerwavelength and a center frequency of a transmitted pulse, respectively.As described in the second embodiment, a target shape is estimated froman obtained quasi-wavefront using Expression (16).

Here, a pseudonoise sequence used as a transmitting waveform will bedescribed in detail. FIG. 5 is a diagram showing a k-stage LinearFeedback Shift Register (LFSR) which generates PN codes. Among thebinary PN codes generated by the circuit of FIG. 5, those whosecoefficient polynominal is a primitive polynominal in a Galois fieldGF(2) are referred to as M-sequences, and have a maximum period of2^(k)−1. A pair of M-sequences whose maximum cross-correlation valuesatisfies the lower limit of Welch of the following expression (17)which is a theoretical limit, is referred to as a preferred pair ofM-sequences.

$\begin{matrix}{R_{\max} \leqq {N{\frac{M - 1}{{NM} - 1}}^{\frac{1}{2}}}} & ( {{Expression}\mspace{14mu} 17} )\end{matrix}$

A Gold sequence is generated by exclusive logical OR operation of apreferred pair of M-sequences. Here, a relative shift amount between thepair of M-sequences is arbitrary, and a larger number of sequences canbe obtained by periodically shifting one of the pair of sequences. It isknown that a cross-correlation between Gold sequences thus obtainedsatisfies the lower limit of Welch. Therefore, in a radar system inwhich N-bit Gold sequences are simultaneously transmitted from Mdevices, a level of range sidelobes expressed on the right side ofExpression (17) unavoidably occurs. Therefore, in this system, when S/Nbecomes a certain large level, the S/(I+N) ratio has a floor, andtherefore, the accuracy of estimation is no longer improved. Therefore,the number of coherent integration times, the noise figure of anamplifier or the like needs to be designed, taking the lower limit ofWelch into consideration.

A preferred pair of M-sequences M1 [n] and M2 [n] (n=1, 2, . . . , and2047) used in this embodiment are generated by primitive polynominals:G ₁(a)=a ¹¹ +a ⁹+1  (Expression 18)G ₂(a)=a ¹¹ +a ⁹ +a ⁶ +a ³+1  (Expression 19)

Note that all the initial register values are set to 1. The i-th Goldsequence is generated as Gi[n]=M1[n]+M2[n+i] using these M-sequences.Among the Gold sequences generated by the aforementioned method, thosehaving i=1, 2, . . . , and 18 are assigned to the transmitting antennas.

An example application of high-speed radar imaging will be described asa more specific example in detail. The system described in thisembodiment is a radar system having the same configuration as that ofthe shape measurement instrument of FIG. 4 having eighteen transmittingantennas and a single receiving antenna. As spread codes, eighteencodes, i.e., 0th code to 17th code, of 2047 chip Gold sequences areused. An antenna interval is a distance corresponding to one chip of aspread code. For example, in the case of 2.5 Gchip/sec, the antennainterval is 12 cm. In this case, an observation range within which rangealiasing does not occur is about 246 m.

FIG. 6 is a diagram showing an output signal when a correlation processof a received signal and each Gold sequence code in the radar system(shape measurement instrument) of this embodiment. The result of thecorrelation process is shown by a solid line. Note that the true shapeof the object is assumed to be a cylindrical shape shown by a solid linein FIG. 7. In FIG. 7, signals corresponding to the transmitting antennalocations are shown and arranged. Also, a quasi-wavefront extracted bythe shape measurement instrument is shown by a dashed line in FIG. 6.Random components in the background are caused by the range sidelobes ofauto- and cross-correlation functions of the Gold sequences as noise areneglected in this calculation. A shape of the object is estimated byapplying the revised SEABED method to the extracted quasi-wavefront.

According to the shape measurement instrument of this embodiment, it canbe seen from FIG. 7 that, whereas a degradation in accuracy of shapeestimation due to an influence of range sidelobes is confirmed, a shapecan be substantially correctly estimated. Also, a feature of themeasurement method of this embodiment is that shape estimation can beachieved by a single snapshot, whereby a shape of an object can bequickly measured.

(Fourth Embodiment)

The shape estimation performance which is obtained when the revisedSEABED method is applied to a code-division UWB radar employing Goldsequence codes, has been heretofore described using an example ofnumerical calculation in which only scattered waveforms are taken intoconsideration. However, in fact, direct waves which are transmitted froma transmitting antenna and are directly received by a receiving antennawithout being scattered by a target object, have an influence on theperformance of the radar. The effect of direct waves is moderate ifantennas used have relatively high directionality like horn antennas.However, if small antennas, such as patch antennas or the like, areused, the influence of direct waves is large and cannot be neglected.Therefore, in a fourth embodiment, the influence of direct waves on theshape estimation performance of the proposed system is quantitativelyevaluated, and an appropriate set of codes for suppressing the influenceis provided. A shape estimation system model similar to that of thethird embodiment is used.

FIG. 8 is a diagram showing a received signal obtained by despreadingdirect waves. In FIG. 8, it can be seen that range sidelobes aresubstantially uniformly distributed at locations other than peaks ofdirect waves. Also, FIG. 9 is a diagram showing a received signal, wheredirect waves have a power which is larger than scattered waves by about10 dB. In this case, a part of waveforms of scattered waves is changedas the sidelobes of the direct waves overlap the scattered waves. Atarget shape estimated from the received signal of FIG. 9 is shown inFIG. 10. It can be seen that a degradation in accuracy of an estimatedimage is larger than that of FIG. 7, and therefore, the influence of thesidelobes of the direct waves at an assumed level on the shapeestimation performance cannot be neglected.

Therefore, the present inventors sought an appropriate set of codes soas to suppress the influence of the sidelobes of the direct waves. Thereceiving timing of each received direct wave is fixed because thedistance between transmission and receiving antennas is fixed. Makinguse of this characteristic, the present inventors contemplated to select18 codes whose direct waves' range sidelobes cancel each other. This issimilar to an idea that a pair of complementary codes cancel thesidelobes of autocorrelation functions, thereby achieving a highresolution.

There are 2049 assumed Gold sequences (codes), and 18 suitable codes areselected from them. In addition, as the transmission timing of each codeis arbitrary, the degree of freedom of periodic shifting of each code isutilized. On the other hand, range sidelobes only near the antennas aresuppressed because it is not necessary to suppress all range sidelobes.This is because the shape estimation by the SEABED method does not workfor targets which are sufficiently distant with respect to the width ofthe antenna array because the locations of the scattering centers aresubstantially not changed even if the locations of the transmittingantennas are changed. Therefore, only distance measurement is performedfor distant targets, and imaging as well as distance measurement areperformed for targets near the antennas. Note that, for distant targets,by averaging 18 received signals, the influence of the range sidelobescan be reduced to enhance the accuracy of the distance measurement.Here, the strategy that codes to be transmitted are selected from Goldsequences instead of searching general codes is adopted for thefollowing reason. As long as Gold sequences are used, autocorrelationfunctions close to impulses and low-level asynchronous cross-correlationfunctions (minimum characteristics) can be guaranteed. Moreover, aperiod of time required for search can be reduced by limiting codes.

Thus, an evaluation function for code selection is expressed by:

$\begin{matrix}{{minimize}_{c_{1},c_{2},\mspace{11mu}\ldots\mspace{14mu},c_{M}}{\sum\limits_{M = 1}^{M}{\sum\limits_{l = 1}^{L}\{ {\sum\limits_{n = 1}^{M}{r_{m,n}(l)}} \}^{2}}}} & ( {{Expression}\mspace{14mu} 20} )\end{matrix}$

Note that r_(m, n)(l) is the cross-correlation function of codes c_(m)and c_(n), M is the number of codes, L is the number of chips where thesidelobes are suppressed. In the system described in this embodiment,for example, M=2049 and L=9. For example, if the chip rate is assumed tobe 2.5 Gchip/s, high-accuracy imaging is performed within the range ofabout 1 m of the antennas, and only distance measurement is performed inareas beyond this range, i.e., an adaptive process depending on thedistance is assumed. Note that, when optimization of Expression (20) isperformed by full search, the evaluation function needs to be calculatedT_(cal)=₂₀₄₉C₁₈·2047¹⁸ times. This full-search calculation requiresabout 1093 years using a computer having a single Xeon 2.8-GHzprocessor, which is completely unrealistic. Therefore, it is desirableto find a suboptimum solution. Here, a greedy algorithm will bediscussed as a technique for optimizing the aforementioned evaluationfunction. The greedy method is a technique of successively andindependently optimizing each variable for multivariable optimization,and is known as an approximation method for combinatorial optimization.Hereinafter, a specific procedure for applying the greedy method to thisoptimization will be described. Note that ran(n) hereinafter means auniform random integer between 1 and n.

(1) Generate ran(2049) 18 times. Go to (2).

(2) If there is a duplicate pair of numbers in 18 random numbers, go to(1). Otherwise, set the 18 random numbers as initial Gold code numbersfor the antennas and go to (3).

(3) Generate ran(2047) 18 times. Set the 18 random numbers as initialcode shift values for the antennas and go to (4).

(4) Calculate and store an evaluation value as a minimum evaluationvalue and store the codes. Go to (5).

(5) Generate ran(18), ran(2049), and ran(2047). Change a Gold codenumber and a code shift for the ran(18)-th antenna to ran(2049) andran(2047). Go to (6).

(6) If there is a duplicate pair of numbers in the 18 antenna codenumbers, go to (5). Otherwise, calculate an evaluation value. Go to (7).

(7) If the evaluation value is smaller than the minimum evaluationvalue, set the evaluation value as a new minimum evaluation value andstores the codes. Otherwise, cancel the change by substituting thestored codes for the current codes. Go to (5).

After performing the aforementioned process a predetermined number oftimes, finally stored codes are adopted for the radar system. Acalculation time required for the code search depends approximately onthe number of times of call of the evaluation function. FIG. 11 shows arelationship between the number of times of call of the evaluationfunction and the evaluation value. FIG. 11 shows the results of both thefull search (closed squares) and the greedy method (open circles). Itcan be seen from FIG. 11 that the greedy method effectively solves thisoptimization problem and suppresses the normalized sidelobe level toabout 16% compared to before the optimization. Specifically, by usingthis proposed codes, the S/I ratio can be improved by about 8 dB in thevicinity of the antennas without the need of additional cost.

The proposed codes found out by the aforementioned technique were usedto investigate the imaging performance of the UWB radar system (shapemeasurement instrument) of this embodiment. FIG. 12 is a diagram showinga signal obtained by despreading direct waves using the codes obtainedby the technique of this embodiment. According to comparison of FIG. 12and FIG. 8, it was confirmed that the sidelobe levels become lowerwithin an area of 3.6 nsec on the right side of each peak when thetechnique of this embodiment is used.

Note that FIG. 13 is a diagram showing a received signal includingscattered waves. It can be seen that, in FIG. 13, the peaks of thescattered waves can be more clearly confirmed than in FIG. 9, andtherefore, the S/I ratio is improved. An estimated shape obtained by therevised SEABED method using this signal is shown in FIG. 14. It can beseen that the measurement accuracy is more improved in FIG. 14 than inFIG. 10.

It was demonstrated that, by selecting the aforementioned codes, theinfluence of direct waves can be reduced and highly accurate imaging canbe achieved.

Although the shape measurement instruments of the second to fourthembodiments each include a large number of transmitters and a singlereceiver, each shape measurement instrument may include a plurality oftransmitters each having a transmitting antenna and a plurality ofreceivers each having a receiving antenna provided at a locationdifferent from those of the transmitters. In this case, if each receivercan receive signals from the plurality of transmitters, the number ofcombinations of signal paths from a transmitter to a receiver isincreased, and therefore, the resolution can be improved. As a result,the total number of receivers and transmitters can be reduced, leadingto a further reduction in cost.

Industrial Applicability

The shape measurement instrument and method of the present invention areapplicable, as means for avoiding danger or the like, to variousapparatuses, such as automobiles, ships, aircrafts, robots and the like.

What is claimed is:
 1. A shape measurement instrument comprising: aplurality of transmitters configured to generate signals expressed as anorthogonal function system or a quasi-orthogonal function system, andradiate the signals having different waveforms or phases; a receiverconfigured to receive the signal reflected from a target object; acorrelation unit configured to obtain a correlation waveform of awaveform of the signal received by the receiver and the signal radiatedby the transmitter radiating the received signal of the plurality oftransmitters; and a shape estimation unit configured to extract aquasi-wavefront based on a plurality of the correlation waveformsobtained by the correlation unit, and estimate a shape of the targetobject based on a relationship between the quasi-wavefront and the shapeof the target object, wherein the transmitter has a transmitting antennaconfigured to transmit the signal, the receiver has a receiving antennaconfigured to receive the signal, the receiving antenna being providedat a location different from that of the transmitting antenna, thelocation of the transmitting antenna is (2X, 0) and the location of thereceiving antenna is (0, 0), a location of a scattering point on aboundary of the target object which contacts an ellipse whose focusesare (2X, 0) and (0, 0) and whose major axis has a length of 2Y is (x,y), and a derivative dY/dX is Y′, the shape estimation unit converts alocation relationship (X, Y) between a time delay and the location ofthe transmitting antenna to the location (x, y) of the scattering pointby: $\begin{matrix}{{x = \frac{{( {X^{2} + Y^{2}} )\overset{.}{Y}} - {2{XY}}}{{X\overset{.}{Y}} - Y}}{y = {{\frac{Y^{2} - X^{2}}{Y - {X\overset{.}{Y}}}}\sqrt{1 - {\overset{.}{Y}}^{2}}}}} & ( {{Expression}\mspace{14mu} 16} )\end{matrix}$ thereby estimating the shape of the target object.
 2. Theshape measurement instrument of claim 1, wherein the signal has afractional bandwidth of 20% or more, the fractional bandwidth being aratio of an occupied bandwidth to a center frequency.
 3. The shapemeasurement instrument of claim 1, wherein the signal is a UWB signal.4. The shape measurement instrument of claim 1, wherein the signal ismodulated using a PN code which is a pseudonoise sequence.
 5. The shapemeasurement instrument of claim 4, wherein the signal is modulated usingan M-sequence code.
 6. The shape measurement instrument of claim 5,wherein the plurality of transmitters radiate M-sequence codes havingdifferent phases.
 7. The shape measurement instrument of claim 4,wherein the signal is modulated using a Gold sequence code.
 8. The shapemeasurement instrument of claim 4, wherein the signal is modulated usinga Kasami sequence code.
 9. The shape measurement instrument of claim 1,wherein the number of the receivers is one.
 10. The shape measurementinstrument of claim 1, wherein a plurality of the receivers areprovided, and each receiver receives the signals radiated from theplurality of transmitters.
 11. A method for measuring a shape using ashape measurement instrument including a plurality of transmitters, areceiver configured to receive a signal reflected from a target object,a correlation unit, and a shape estimation unit, the method comprisingthe steps of: (a) radiating signals having different waveforms or phasesexpressed as an orthogonal function system or a quasi-orthogonalfunction system by the plurality of transmitters; (b) receiving thesignals reflected from the target object by the receiver; (c) obtaininga correlation waveform of a waveform of the signal received by thereceiver and the signal radiated by the transmitter radiating thereceived signal of the plurality of transmitters, by the correlationunit; (d) obtaining extremums of the correlation waveform by the shapeestimation unit; (e) connecting adjacent ones of the extremums togenerate a quasi-wavefront by the shape estimation unit; (f) extractinga true quasi-wavefront from the quasi-wavefront by the shape estimationunit; and (g) estimating a shape of the target object from the truequasi-wavefront by the shape estimation unit, wherein the plurality oftransmitters each have a transmitting antenna configured to transmit thesignal, the receiver has a receiving antenna configured to receive thesignal, the receiving antenna being provided at a location differentfrom that of the transmitting antenna, the location of the transmittingantenna is (2X, 0) and the location of the receiving antenna is (0, 0),a location of a scattering point on a boundary of the target objectwhich contacts an ellipse whose focuses are (2X, 0) and (0, 0) and whosemajor axis has a length of 2Y is (x, y), and a derivative dY/dX is Y′,in step (g), the following expression: $\begin{matrix}{{x = \frac{{( {X^{2} + Y^{2}} )\overset{.}{Y}} - {2{XY}}}{{X\overset{.}{Y}} - Y}}{y = {{\frac{Y^{2} - X^{2}}{Y - {X\overset{.}{Y}}}}\sqrt{1 - {\overset{.}{Y}}^{2}}}}} & ( {{Expression}\mspace{14mu} 16} )\end{matrix}$ is used to estimate the shape of the target object. 12.The method of claim 11, wherein the signal is modulated using a PN codewhich is a pseudonoise sequence.
 13. The method of claim 11, wherein thenumber of the receivers included in the shape measurement instrument isone.
 14. The method of claims 11, wherein the shape measurementinstrument includes a plurality of the receivers, and in step (b), eachreceiver receives the signals radiated from the plurality oftransmitters.
 15. The method of claim 12, wherein the signal ismodulated using a Gold sequence code.
 16. The method of claim 15,further comprising: (h) before step (a), selecting a combination ofcodes which reduces an influence of a direct wave which is transmittedfrom each of the transmitters and is received by the receiver withoutvia the target object, wherein, in step (a), the plurality oftransmitters transmit the combination of codes selected in step (h).